FOXBOROUGH — The two quarterbacks may be getting old, but the annual showdowns between Tom Brady and Peyton Manning never do.

Can you get sick of listening to Beethoven? Or tired of watching Michael Jordan highlights? There is no such thing as Brady-Manning ennui.

Just when you thought the two Canton-bound, iconic quarterbacks couldn’t add anything to their storied rivalry they did on a frigid Sunday night. For the first time, Brady v. Manning couldn’t be decided in regulation. Brady-Manning XIV had to go to overtime, and just when it was destined for a deadlocked decision, the Patriots exited with a bizarre 34-31 decision.

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The annual game between career counterparts Brady and Manning was like one of those Russian nesting dolls. It was game within a game within a game within a game.

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The decisive play had nothing to do with either of the preeminent passers, though. It came when former Patriot Tony Carter had a Ryan Allen punt bounce off him and the Patriots recovered at the Denver 13. Stephen Gostkowski hit a 31-yard field goal to end a game that froze time and a lot of fingers and toes with 1:56 left in overtime.

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This had to be one of, if not, the strangest of the Brady-Manning play dates.

The teams combined for 11 fumbles, six in the first half by the Patriots. Manning (19 of 36 for 150 yards, two touchdowns, one interception) didn’t break 100 yards passing until the fourth quarter. The Broncos rushed for 280 yards. The Patriots trailed, 24-0, at halftime. They took a 28-24 lead with 13:13 left. They led, 31-24, with three and a half minutes to go. Then they appeared destined for a tie.

Maybe, some of those write-in votes that went to David Ortiz for mayor of Boston should have gone to Brady.

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Brady won his 10th game against Manning, and for one game at least, he decisively won the debate about who is better. Unlike the game, it was no contest.

Brady was 34 of 50 for 344 yards and three touchdowns, all of which came in the second half. After halftime, he was 24 for 33 for 263 yards.

“We didn’t give ourselves a chance in the first half with the turnovers. They got a big lead,” said Brady. “We found a way to put one play in front of the next one and the next one.”

It can’t be a duel if one of the participants can’t get his gun out of his holster. Like the weather, Manning was chilly. He was a far cry from the quarterback who had terrorized the NFL with an indomitable air show through his first 10 games — until the Patriots took a 31-24 lead.

Manning marched the Broncos 80 yards in 10 plays to tie the game with 3:06 left. He hit Demaryius Thomas with an 11-yard touchdown with 3:06 left.

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After all that talk about Luke Kuechly holding Rob Gronkowski at the end of the Patriots’ loss to the Panthers last Monday, it was a lack of holding that put the Fighting Belichicks in a hole against Denver.

They couldn’t hold on to the football. They couldn’t hold their ground against the Denver running game, and they couldn’t hold their own in a nationally-televised showdown. They were down, 24-0, at halftime.

It was like the football was coated in Teflon in the first half for the Patriots. It just didn’t stick. The Patriots turned the ball over on their first three possessions, all fumbles. They led directly to 17 first-quarter Denver points.

Manning’s fingerprints were barely on the Broncos’ lead. He threw the ball just three times as Denver built its 17-0 advantage.

“Our running game was working, so that’s what we were going with,” said Manning. “When you’re running the ball well, that’s a good thing.”

Manning wasn’t even on the field for the first of Denver’s scores Stevan Ridley fumbled yet again and Von Miller scooped it up and ran it back 60 yards for a touchdown with 9:54 left in the first quarter.

On the second play of the Patriots’ ensuing possession, Brady was strip-sacked by Miller. Two plays later, Knowshon Moreno (37 rushes for 224 yards) scored on a 2-yard touchdown run to make it 14-0, before Manning even had double-digit passing yards.

A LeGarrette Blount fumble set up a 27-yard field goal from Matt Prater that made 17-0.

Just when you were ready to write the latest Brady-Manning meeting as a debacle, Brady turned it into a spectacle.

TB12 marched the Patriots down the field on the opening drive of the second half, completing all seven of his passes. The last pass was a delivered with laser-guided precision, dropping into the arms of Julian Edelman for a 5-yard touchdown that cut the Denver lead to 24-7.

A Montee Ball fumble set up a 1-yard touchdown by Brandon Bolden.

The Broncos’ next drive short-circuited when Manning fumbled the ball untouched on third and 5 from his own 42. Brady hit Edelman with a 43-yard pass to move the ball to the Denver 8. On third and goal, Brady sizzled a pass that crackled the cool air and landed in the arms of Gronkowski. The deficit was just 3 (24-21).

A patented Peyton interception to Logan Ryan on Denver’s next possession followed.

Brady threw a short pass to Edelman, who left a vapor trail as he juked Broncos cornerback Chris Harris Jr. and scored a 14-yard touchdown. A frozen pipe-dream at halftime — a Patriots lead — was a reality with 13:13 left.

Who knows how many of these Brady-Manning duels are left.

So, bonus football featuring the two Hall of Famers was worth the wait. Watching them face off never gets old.